Recently we have demonstrated that conventional (free-space) Faraday rotation spectroscopy (FRS) can be successfully transitioned into optical fiber-based sensing architectures using paramagnetic gas-filled hollow-core photonic bandgap fibers (HC-PCFs)<sup>1</sup>. Our measurements revealed that due to the birefringence properties of the HC-PCFs, behavior of the fiber-optic FRS signals is substantially different compared to free-space FRS systems. Furthermore, magnetic circular dichroism tends to have much higher influence on the FRS signals than in other systems. To explain this behavior we have developed a theoretical model, and shown that close agreement with the experimental data can be achieved. In this paper we focus attention on the detailed explanation and the in-depth discussion of the model and assumptions incorporated within it. This approach can be easily extended to account for parasitic effects that take place in real-world FRS sensor systems such as imperfect polarizers or birefringent gas cell windows.
Microstructured optical fibers provide a unique environment for new compact sensing of gases as they offer advantages including long optical pathlengths, strong confinement of high power light and extremely small sample volumes compared to free-space gas sensing architectures. Here we investigate the interaction of a modulated magnetic field with guided light to detect a paramagnetic active gaseous medium within a hollow-core photonic bandgap fiber (HC-PCF). This novel fiber-optic approach to Faraday Rotation Spectroscopy (FRS) demonstrates the detection of molecular oxygen at 762.309 nm with nano-liter detection volume. By using a differential detection scheme for improved sensitivity, guided-mode FRS spectra were recorded for different coupling conditions of the light (i.e., different light polarization angles) and various gas sample pressures. The observed FRS signal amplitudes and shapes are influenced by the structural properties of the fiber, and magneto-optical properties of the gas sample including the magnetic circular birefringence (MCB) and the magnetic circular dichroism (MCD). A theoretical model has been developed to simulate such FRS signals, which are in good agreement with the observed experimental results and provide a first understanding of guided-mode FRS signals and dynamics of the magneto-optical effects inside the optical fiber. The results show that microstructured optical fibers can offer a unique platform for studies concerning the propagation of light in linearly and circularly birefringent media.